The government had sought to make it more difficult for detainees who lost their habeas cases to continue to see their lawyers and more difficult for those lawyers to advocate for their clients, including by bringing new petitions based, for example, on new information or changed circumstances.See here and here for a discussion of a recent district ruling in the continuing attempt of Gitmo lawyers to obtain some court access for their clients. The D.C. Court of Appeals, the ultimate authority while the USSC in effect ignores the area, partially because Kagan is recused, leading to likely 4-4 rulings at best even if Kennedy finds some case of overreaching. The basic right even to bring a petition and the ability to see lawyers concerning the potential needs here (functionally, for those in Gitmo, the second leads from the first) is at stake here.
Kennedy wrote Boumediene to provide some basic federal judicial oversight, but various D.C. court of appeals judges have little respect for that ruling, applying it in ways many think overly narrow. Basically, as I have noted in the past, even if you want the President to need to go to court before using drones against people, the result might be more form than substance. Still, there continues to be some protections in place here, limited as they might seem, and the basic right to have lawyers, lawyers who bring their cases to court and to the public's view too puts pressure on the government as well.
This looks to be an important case to the degree it reaffirms the basic principles at place. As noted in a link, the opinion is well worth reading, clearly and firmly argued. The opinion reaffirms the fundamental nature of habeas corpus, a check on executive power that goes back to principles set forth in the 13th Century, along with what is needed for it to have much value. Gitmo defendants aren't going to be able to really bring these things pro se or something. It cites an interesting case where the USSC protected the right to obtain help from jailhouse inmates, the oral argument here,* and Justice Douglas having a worthwhile concurrence on the need of assistance to defend one's rights, including not only lawyers.
Lawyers are at stake here, but various cases here underline the importance of others as well, including media forces, private organizations and many others. The basic ability to advocate, which includes some access in various respects, follows from this. I would add that this underlines, contra some comments by Glenn Greenwald and the like, something as limited as transporting people from GITMO to domestic maximum security facilities (an Obama proposal blocked on a bipartisan basis) is valuable. Having people in some facility in Illinois leads to easier access to all.
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* Good oral argument, including discussing the common law right of layman to assist in petitioning relief (the 1A right to petition was expressly cited and habeas / access to the courts generally is a form of this often ignored aspect of the amendment) with certain exceptions noted.